A mathematical diagnostic drilling model was derived from the balance of forces acting at the PDC bit cutter. The model combined the torque and the drilling rate equations, cutter's geometry and rock properties. It was verified using the laboratory drilling data from several research reports as 11 as the field drilling data collected by the authors. Based on the drilling model, a new method was developed for the in-situ measurements of the PDC bit condition and for the lithology change detection. In this technique, a diagnostic plot is made by correlating two dimensionless groups containing measured values of torque, weight on bit, rotary speed and penetration rate. Several laboratory and field data (presented in the study) confirmed linearity of such a plot. The diagnostic plot is a unique indicator of the bit-rock interaction and it is independent from the bit operational variables. Moreover, the instantaneous wear of a PDC bit can be computed from coordinates of the straight line points. This method is feasible for a graphical use supplemented with a computer program. The technique was further verified by comparing the predicted and the measured PDC bit wear from the MWD records in the Gulf Coast area. Also provided, were the examples of a correlation between rapid formation changes and discontinuities in the diagnostic plots. The new method contributes to the PDC bit drilling theory. Its importance lies in the MWD software development for the purpose of the in-situ rock detection and the PDC bit evaluation and control. Introduction Polycrystalline Diamond Compact (PDC) bits are a high-tech revival of the earliest bit types, drag bits. By using the state of the art materials, drag bits have been competitively reintroduced into the oil well milling technology. Absence of moving parts and the high wear resistance of synthetic diamonds make a drag bit a long lasting bottomhole tool. The success of the PDC's in the petroleum drilling industry is well documented in the literature. PDC bits are extremely sensitive to formation properties and operating conditions. Recent studies on PDC drilling performance in the harsh environment such as geothermal and hard rock drilling showed an average two-fold increase of penetration rate and bit life as compared to conventional bits, which resulted in cost reduction 10 to 15%. However, in the case where the PDC bit life was reduced 50%, the cost savings were cut in half. Therefore there is a very good reason to improve bit life in any potential application of PDC bits, in order to take advantage of their high penetration rates. Early detection of formation changes and appropriate adjustment of the operational variables are very important measures to save the bit. Such detection can be made possible with the instantaneous drilling data acquisition (MWD) system. Development of the drilling data acquisition systems has been in progress for many years in the petroleum industry. However, without having an appropriate data processing tool (a drilling model), some of the information will become invaluable. To date, a few predictive models have been proposed. Ziaja developed a mathematical model of a single PDC cutter penetration assuming a circular cut and an absence of cutters interaction. The model was designed for a core bit. The single proportionality constant was used to up-scale from the single cutter load and penetration to the weight on bit and drilling rate. Data from one field run of a core bit was used to verify the model. Glowka used experimental data from laboratory drilling in hard rocks and developed a power-function correlation between cutter penetration and stress at the wearflat area. His analytical work also included derivation of the single cutter wear equation as a function of penetration per rotation and footage. P. 137^

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